arXiv subjects

Bezirgen Veliyev

Publications and source records attributed to Bezirgen Veliyev.

14 recordsLinked to original sources

arXiv2026

The realized empirical distribution function of stochastic variance with application to goodness-of-fit testing

We propose a nonparametric estimator of the empirical distribution function (EDF) of the latent spot variance of the log-price of a financial asset. We show that over a fixed time span our realized EDF (or REDF) -- inferred from noisy high-frequency data -- is consistent as the mesh of the observation grid goes to zero. In a double-asymptotic framework, with time also increasing to infinity, the REDF converges to the cumulative distribution function of volatility, if it exists. We exploit these results to construct some new goodness-of-fit tests for stochastic volatility models. In a Monte Carlo study, the REDF is found to be accurate over the entire support of volatility. This leads to goodness-of-fit tests that are both correctly sized and relatively powerful against common alternatives. In an empirical application, we recover the REDF from stock market high-frequency data. We inspect the goodness-of-fit of several two-parameter marginal distributions that are inherent in standard stochastic volatility models. The inverse Gaussian offers the best overall description of random equity variation, but the fit is less than perfect. This suggests an extra parameter (as available in, e.g., the generalized inverse Gaussian) is required to model stochastic variance.

econ.EM↗

arXiv2026

Inference from high-frequency data: A subsampling approach

In this paper, we show how to estimate the asymptotic (conditional) covariance matrix, which appears in central limit theorems in high-frequency estimation of asset return volatility. We provide a recipe for the estimation of this matrix by subsampling; an approach that computes rescaled copies of the original statistic based on local stretches of high-frequency data, and then it studies the sampling variation of these. We show that our estimator is consistent both in frictionless markets and models with additive microstructure noise. We derive a rate of convergence for it and are also able to determine an optimal rate for its tuning parameters (e.g., the number of subsamples). Subsampling does not require an extra set of estimators to do inference, which renders it trivial to implement. As a variance-covariance matrix estimator, it has the attractive feature that it is positive semi-definite by construction. Moreover, the subsampler is to some extent automatic, as it does not exploit explicit knowledge about the structure of the asymptotic covariance. It therefore tends to adapt to the problem at hand and be robust against misspecification of the noise process. As such, this paper facilitates assessment of the sampling errors inherent in high-frequency estimation of volatility. We highlight the finite sample properties of the subsampler in a Monte Carlo study, while some initial empirical work demonstrates its use to draw feasible inference about volatility in financial markets.

econ.EM↗

arXiv2026

A machine learning approach to volatility forecasting

We inspect how accurate machine learning (ML) is at forecasting realized variance of the Dow Jones Industrial Average index constituents. We compare several ML algorithms, including regularization, regression trees, and neural networks, to multiple Heterogeneous AutoRegressive (HAR) models. ML is implemented with minimal hyperparameter tuning. In spite of this, ML is competitive and beats the HAR lineage, even when the only predictors are the daily, weekly, and monthly lags of realized variance. The forecast gains are more pronounced at longer horizons. We attribute this to higher persistence in the ML models, which helps to approximate the long-memory of realized variance. ML also excels at locating incremental information about future volatility from additional predictors. Lastly, we propose a ML measure of variable importance based on accumulated local effects. This shows that while there is agreement about the most important predictors, there is disagreement on their ranking, helping to reconcile our results.

econ.EM↗

arXiv2026

Warp speed price moves: Jumps after earnings announcements

Corporate earnings announcements unpack large bundles of public information that should, in efficient markets, trigger jumps in stock prices. Testing this implication is difficult in practice, as it requires noisy high-frequency data from after-hours markets, where most earnings announcements are released. Using a unique dataset and a new microstructure noise-robust jump test, we show that earnings announcements almost always induce jumps in the stock price of announcing firms. They also significantly raise the probability of price co-jumps in non-announcing firms and the market. We find that returns from a post-announcement trading strategy are consistent with efficient price formation after 2016.

econ.EM↗

arXiv2024

Treatment Evaluation at the Intensive and Extensive Margins

This paper provides a solution to the evaluation of treatment effects in selective samples when neither instruments nor parametric assumptions are available. We provide sharp bounds for average treatment effects under a conditional monotonicity assumption for all principal strata, i.e. units characterizing the complete intensive and extensive margins. Most importantly, we allow for a large share of units whose selection is indifferent to treatment, e.g. due to non-compliance. The existence of such a population is crucially tied to the regularity of sharp population bounds and thus conventional asymptotic inference for methods such as Lee bounds can be misleading. This problem can be solved using smoothed outer identification regions for inference. We provide semiparametrically efficient debiased machine learning estimators for both regular and smooth bounds that can accommodate high-dimensional covariates and flexible functional forms. Our study of active labor market policy reveals the empirical prevalence of the aforementioned indifference population and supports results from previous impact analyses under much weaker assumptions.

econ.EM↗

arXiv2022

Treatment recommendation with distributional targets

We study the problem of a decision maker who must provide the best possible treatment recommendation based on an experiment. The desirability of the outcome distribution resulting from the policy recommendation is measured through a functional capturing the distributional characteristic that the decision maker is interested in optimizing. This could be, e.g., its inherent inequality, welfare, level of poverty or its distance to a desired outcome distribution. If the functional of interest is not quasi-convex or if there are constraints, the optimal recommendation may be a mixture of treatments. This vastly expands the set of recommendations that must be considered. We characterize the difficulty of the problem by obtaining maximal expected regret lower bounds. Furthermore, we propose two (near) regret-optimal policies. The first policy is static and thus applicable irrespectively of subjects arriving sequentially or not in the course of the experimentation phase. The second policy can utilize that subjects arrive sequentially by successively eliminating inferior treatments and thus spends the sampling effort where it is most needed.

econ.EM↗

arXiv2020

A GMM approach to estimate the roughness of stochastic volatility

We develop a GMM approach for estimation of log-normal stochastic volatility models driven by a fractional Brownian motion with unrestricted Hurst exponent. We show that a parameter estimator based on the integrated variance is consistent and, under stronger conditions, asymptotically normally distributed. We inspect the behavior of our procedure when integrated variance is replaced with a noisy measure of volatility calculated from discrete high-frequency data. The realized estimator contains sampling error, which skews the fractal coefficient toward "illusive roughness." We construct an analytical approach to control the impact of measurement error without introducing nuisance parameters. In a simulation study, we demonstrate convincing small sample properties of our approach based both on integrated and realized variance over the entire memory spectrum. We show the bias correction attenuates any systematic deviance in the parameter estimates. Our procedure is applied to empirical high-frequency data from numerous leading equity indexes. With our robust approach the Hurst index is estimated around 0.05, confirming roughness in stochastic volatility.

q-fin.ST↗

arXiv2020

Functional Sequential Treatment Allocation

Consider a setting in which a policy maker assigns subjects to treatments, observing each outcome before the next subject arrives. Initially, it is unknown which treatment is best, but the sequential nature of the problem permits learning about the effectiveness of the treatments. While the multi-armed-bandit literature has shed much light on the situation when the policy maker compares the effectiveness of the treatments through their mean, much less is known about other targets. This is restrictive, because a cautious decision maker may prefer to target a robust location measure such as a quantile or a trimmed mean. Furthermore, socio-economic decision making often requires targeting purpose specific characteristics of the outcome distribution, such as its inherent degree of inequality, welfare or poverty. In the present paper we introduce and study sequential learning algorithms when the distributional characteristic of interest is a general functional of the outcome distribution. Minimax expected regret optimality results are obtained within the subclass of explore-then-commit policies, and for the unrestricted class of all policies.

econ.EM↗

arXiv2020

Functional Sequential Treatment Allocation with Covariates

We consider a multi-armed bandit problem with covariates. Given a realization of the covariate vector, instead of targeting the treatment with highest conditional expectation, the decision maker targets the treatment which maximizes a general functional of the conditional potential outcome distribution, e.g., a conditional quantile, trimmed mean, or a socio-economic functional such as an inequality, welfare or poverty measure. We develop expected regret lower bounds for this problem, and construct a near minimax optimal assignment policy.

stat.ML↗

arXiv2018

Edgeworth expansion for Euler approximation of continuous diffusion processes

In this paper we present the Edgeworth expansion for the Euler approximation scheme of a continuous diffusion process driven by a Brownian motion. Our methodology is based upon a recent work \cite{Yoshida2013}, which establishes Edgeworth expansions associated with asymptotic mixed normality using elements of Malliavin calculus. Potential applications of our theoretical results include higher order expansions for weak and strong approximation errors associated to the Euler scheme, and for studentized version of the error process.

math.PR↗

arXiv2015

Edgeworth expansion for the pre-averaging estimator

In this paper, we study the Edgeworth expansion for a pre-averaging estimator of quadratic variation in the framework of continuous diffusion models observed with noise. More specifically, we obtain a second order expansion for the joint density of the estimators of quadratic variation and its asymptotic variance. Our approach is based on martingale embedding, Malliavin calculus and stable central limit theorems for continuous diffusions. Moreover, we derive the density expansion for the studentized statistic, which might be applied to construct asymptotic confidence regions.

math.ST↗

arXiv2012

Utility Maximization in a Binomial Model with transaction costs: a Duality Approach Based on the Shadow Price Process

We consider the problem of optimizing the expected logarithmic utility of the value of a portfolio in a binomial model with proportional transaction costs with a long time horizon. By duality methods, we can find expressions for the boundaries of the no-trade-region and the asymptotic optimal growth rate, which can be made explicit for small transaction costs. Here we find that, contrary to the classical results in continuous time, the size of the no-trade-region as well as the asymptotic growth rate depend analytically on the level of transaction costs, implying a linear first order effect of perturbations of (small) transaction costs. We obtain the asymptotic expansion by an almost explicit construction of the shadow price process.

q-fin.PM↗

arXiv2010

A short Proof of the Doob-Meyer Theorem

Every submartingale S of class D has a unique Doob-Meyer decomposition S=M+A, where M is a martingale and A is a predictable increasing process starting at 0. We provide a short and elementary prove of the Doob-Meyer decomposition theorem. Several previously known arguments are included to keep the paper self-contained.

math.PR↗

arXiv2010

A Direct Proof of the Bichteler--Dellacherie Theorem and Connections to Arbitrage

We give an elementary proof of the celebrated Bichteler-Dellacherie Theorem which states that the class of stochastic processes $S$ allowing for a useful integration theory consists precisely of those processes which can be written in the form $S=M+A$, where $M$ is a local martingale and $A$ is a finite variation process. In other words, $S$ is a good integrator if and only if it is a semi-martingale. We obtain this decomposition rather directly from an elementary discrete-time Doob-Meyer decomposition. By passing to convex combinations we obtain a direct construction of the continuous time decomposition, which then yields the desired decomposition. As a by-product of our proof we obtain a characterization of semi-martingales in terms of a variant of \emph{no free lunch}, thus extending a result from [DeSc94].

math.PR↗